N = [2:65, 70:5:200]';
sigma = 0.0001:0.0001:0.01;

k = zeros(1,length(sigma));
for i = 1:length(sigma)
    k(i) = kappaForSigma(sigma(i),N);
end


%x = lsqcurvefit(@fitFunctionForKappa,[1,1],sigma,k);

%plot(sigma,k,sigma,(4.*sigma.*(1+1.49.*sqrt(sigma)-0.92.*sigma.^2))./(pi.*(1-sigma).^2));
%plot(sigma,k,sigma,fitFunctionForKappa(x,sigma));


% k2 = 8*sigma ./ (2*pi - exp(-1/2 * lambertw(-8*sigma)) .* lambertw(-8*sigma));

x = lsqcurvefit(@fitFunctionForb1,0,sigma,k);

k2 = fitFunctionForb1(x,sigma);
%k2 = 4.*sigma./pi;
plot(sigma,k,sigma,k2);

xlabel('\sigma');
ylabel('\kappa');

legend('\kappa Using Numerical H','Asymptotic Kappa Including b_1');
